a) For n > 4, consider the strings made up of n bits — that is, a total of n 0’s and l’...

a) For n > 4, consider the strings made up of n bits — that is, a total of n 0’s and l’s. In particular, consider those strings where there are (exactly) two occurrences of 01. For example, if n = 6 we want to include strings such as 010010 and 100101, but not 101111 or 010101. How many such strings are there?

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b) For n ≥ 6, how many strings of n 0’s and 1 ’s contain (exactly) three occurrences of 01?

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c) Provide a combinatorial proof for the following:

For n ≥ 1,